ESAT Notes and Formula Decks

Module Resources (Clean View)

Compact formulas, prep routines, and a short runway plan. Pick a module, expand its card, then jump to walkthroughs when you want worked examples.

View SpecWalkthroughsESAT Hub

Physics Formula Pack

  • \[s = ut + \frac{1}{2}at^2\]
  • \[v^2 = u^2 + 2as\]
  • \[v = u + at\]
  • \[F = ma\]
  • \[p = mv\]
  • \[F \Delta t = \Delta p\]
  • \[E_k = \frac{1}{2}mv^2\]
  • \[E_p = mgh\]
  • \[W = Fd \cos(\theta)\]
  • \[V = IR\]
  • \[P = IV = I^2R = \frac{V^2}{R}\]
  • Series/parallel R rules
  • \[v = f\lambda\]
  • \[f_n = \frac{nv}{2L}\]
  • Intensity $\propto \frac{1}{r^2}$

Maths 1 Formula Pack

  • Log laws: \[\ln(ab) = \ln a + \ln b\], \[\ln(a^k) = k \ln a\]
  • Quadratics: solutions of \[ax^2 + bx + c = 0\] via discriminant \[b^2 - 4ac\]
  • Trig identities: \[\sin^2 x + \cos^2 x = 1\], \[\tan x = \frac{\sin x}{\cos x}\], \[\sin(A \pm B)\] formulas
  • Differentiation: \[\frac{d(x^n)}{dx} = nx^{n-1}\], \[\frac{d(\ln x)}{dx} = \frac{1}{x}\], \[\frac{d(e^x)}{dx} = e^x\]
  • Integration: \[\int x^n dx = \frac{x^{n+1}}{n+1} + C\] (\[n \neq -1\]), \[\int e^x dx = e^x + C\]

Maths 2 Formula Pack

  • Geometric: \[S_{\infty} = \frac{a}{1-r}\] for \[|r| < 1\]
  • Binomial: \[(1+x)^n = 1 + nx + \frac{n(n-1)}{2}x^2 + \dots\] (\[|x| < 1\])
  • Matrices: \[\det \begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc\]; inverse \[= \frac{1}{ad-bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}\]
  • Complex: \[z = re^{i\theta}\]; modulus \[r\], argument \[\theta\]; Euler: \[e^{i\theta} = \cos\theta + i\sin\theta\]
  • Vectors: \[\mathbf{a} \cdot \mathbf{b} = |\mathbf{a}| |\mathbf{b}| \cos(\phi)\] ; projection of \[\mathbf{a}\] on \[\mathbf{b} = \frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{b}|}\]

Prep Notes

  • No calculator; practise mental arithmetic and clean algebra.
  • Check units and proportionality on every numeric item.
  • Carry a one-page formula sheet; rewrite it weekly from memory.
  • Use walkthroughs to copy the structure, then re-derive cold.
  • Target 90 seconds per item in drills; always guess if unsure.

Study Rhythm

  • Rotate daily: Physics set, Maths 1 set, Maths 2 set.
  • Keep a mistake log tagged by topic and root cause.
  • End sessions with a mixed mini-set to mimic paper shuffle.
  • Refresh formulas and key identities before each block.

Exam Moves

  • First pass: quick wins, skip anything over 90 seconds.
  • Eliminate impossible options; estimate from bounds.
  • Re-read stems for qualifiers (always, must, could).
  • Order-of-magnitude and sign checks before committing.

6-Week Runway (Light)

Weeks 1-2

  • • Rebuild fundamentals (algebra, trig, kinematics).
  • • Make formula flashcards; rewrite twice a week.
  • • 20-30 untimed questions per day.

Weeks 3-4

  • • Timed sets (30-40 mins), mark and rework.
  • • One mixed paper-equivalent weekly.
  • • Update mistake log and flashcards.

Weeks 5-6

  • • Two full timed papers weekly.
  • • Targeted drills on weak tags.
  • • Lock routine: sleep, food, and timing.

← Back to ESAT Hub